If the weather is IMC you are well advised to remain on centerline. If it is
VMC, and your equipment will support parallel track offset, then 1/10 of a mile
is probably going to mitigate your concerns. But, if operating IFR it is
essential to terminate offset operations before beginning an instrument approach
procedure.

If your equipment won't support parallel offset, then your only remaining option
is to fly the autopilot in heading mode and try to keep the XTRK error at some
value approximating 1/10 of a n.m.

Icebound wrote:

In the "good old" VOR days, it must have been pretty difficult to fly down
the centerline of an airway (or of any direct track).

So an eastbound VFR/IFR aircraft descending from 7500/7000 to his
destination, was more than likely to avoid traffic... on the reciprocal
track passing him by at 6500 or 6000... by some significant horizontal
error-distance, even if they didn't see each other (big sky theory :-) ).

GPS horizontal accuracy with WAAS is already in the order of magnitude of a
Cessna's wingspan, and some are talking about getting it down to mere
inches.

So the question is: If my Westbound Cessna at 6000 feet (with the autopilot
keeping it happily on the GPS-track centerline) meets the descending Bonanza
on the reciprocal track between the same two airports (using a similar
GPS/a-p combo), there is a distinct possibility that the horizontal
clearance may be zero...

...so is there anything in the current crop of GPS and/or Autopilot systems
that allow me to maintain a small cross-track error of my choosing, without
actually entering off-navaid-off-airport waypoints? ...or do we care; am I
overly concerned???